Related papers: Function spaces for second-order polynomial time
We prove that there is no 1-complemented subspace of finite codimension in separable rearrangament-invariant function spaces.
We develop a unified second-order parameterized complexity theory for spaces of integrable functions. This generalizes the well-established case of second-order parameterized complexity theory for spaces of continuous functions.…
We continue our study of the global properties of the z=2 Schroedinger space-time. In particular, we provide a codimension 2 isometric embedding which naturally gives rise to the previously introduced global coordinates. Furthermore, we…
The class of functions from the integers to the integers computable in polynomial time has been characterized recently using discrete ordinary differential equations (ODE), also known as finite differences. In the framework of ordinary…
We give a new proof that bounded non-commutative functions on polynomial polyhedra can be represented by a realization formula, a generalization of the transfer function realization formula for bounded analytic functions on the unit disk.
Spacetime is modelled as a homogeneous manifold given by the classes of unitary $\U(2)$ operations in the general complex operations $\GL(\C^2)$. The residual representations of this noncompact symmetric space of rank two are characterized…
We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, preferential union and fixset, we give finite equational or…
We study the computational power of polynomial threshold functions, that is, threshold functions of real polynomials over the boolean cube. We provide two new results bounding the computational power of this model. Our first result shows…
The class of type-two basic feasible functionals ($\mathtt{BFF}_2$) is the analogue of $\mathtt{FP}$ (polynomial time functions) for type-2 functionals, that is, functionals that can take (first-order) functions as arguments.…
We examine two different ways of encoding a counting function, as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input…
We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and…
We study function spaces that are related to square-integrable, irreducible, unitary representations of several low-dimensional nilpotent Lie groups. These are new examples of coorbit theory and yield new families of function spaces on…
We introduce two new operations (compositional products and implication) on Weihrauch degrees, and investigate the overall algebraic structure. The validity of the various distributivity laws is studied and forms the basis for a comparison…
Using an iterative tree construction we show that for simple computable subsets of the Cantor space Hausdorff, constructive and computable dimensions might be incomputable.
We describe the dimensions of low Hochschild cohomology spaces of exceptional periodic representation-infinite algebras of polynomial growth. As an application we obtain that an indecomposable non-standard periodic representation-infinite…
We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional…
In the first part we have shown that, for $L_2$-approximation of functions from a separable Hilbert space in the worst-case setting, linear algorithms based on function values are almost as powerful as arbitrary linear algorithms if the…
We prove that P != NP by proving the existence of a class of functions we call Tau, each of whose members satisfies the conditions of one-way functions. Each member of Tau is a function computable in polynomial time, with negligible…
We present a general prescription for the holographic computation of real-time n-point functions in non-trivial states. In QFT such real-time computations involve a choice of a time contour in the complex time plane. The holographic…
It will be shown that the polynomial time computable numbers form a field, and especially an algebraically closed field.